User`s guide

Using Akaike’s Criteria to Valida te Models
Using Akaike’s Criteria to Validate Models
In this section...
“Definition of FPE” on page 8-61
“Computing FPE ” on page 8-62
“Definition of AIC” o n page 8-62
“Computing AIC ” on page 8-63
Definition of FPE
Akaike’s Final Prediction Error (FPE) criterion provides a measure of model
quality by simulating the situation where the m odel is tested on a different
data set. After computing several d ifferent models, you can compare them
using this criterion. According to Aka ike’s theory, the most accurate model
has the smallest FPE.
Note If you use the same data set for both model estimation and validation,
the fit always improves as you increase the m odel order and, therefore, the
flexibility of the model structure.
Akaike’s Final Prediction E rror (FPE) is defined by the following equation:
FPE V
d
N
d
N
=
+
−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
1
1
where V is the loss function, d is the number of estimated parameters, and N
is the number of values in the estim ation data set.
The toolbox assumes that the final prediction error is asymptotic for d<<N
and uses the following approximation to compute FP E:
FPE V
d
N
=+
()
1
2
The loss fu
nction V is defined by the following eq uation:
8-61